+69 Use Sigma Notation to write the following sums.
a) 1/4 + 3/8 + 7/16 + 15/32 + 31/64
b) 1/2+ 2/4 + 6/8 + 24/16 + 120/32 + 720/64
(Note: Any tips or methods in finding the answer are much apreciated)
+118667 a) 1/4 + 3/8 + 7/16 + 15/32 + 31/64
I noticed that the differentces in the numerator were 2, 4, 8, 16 and these are powers of 2. So...
\(\displaystyle\sum_{n=1}^{n=5}\;\frac{2^n-1}{2^{n+1}}\)
b) 1/2+ 2/4 + 6/8 + 24/16 + 120/32 + 720/64
\(\displaystyle\sum_{n=1}^{n=6}\;\frac{n!}{2^n}\)
+118667 a) 1/4 + 3/8 + 7/16 + 15/32 + 31/64
I noticed that the differentces in the numerator were 2, 4, 8, 16 and these are powers of 2. So...
\(\displaystyle\sum_{n=1}^{n=5}\;\frac{2^n-1}{2^{n+1}}\)
b) 1/2+ 2/4 + 6/8 + 24/16 + 120/32 + 720/64
\(\displaystyle\sum_{n=1}^{n=6}\;\frac{n!}{2^n}\)
